Question

Johnny Inc is currently selling for $50. The firm is expected to pay a dividend of $2 one year from now. Dividends are expected to grow at a constant rate of X% indefinitely. Id the required rate of return of this stock is 12%, what is the growth rate of the dividend (X)? Assume the stock is in equilibrium. 12% 10% 8% 6%

Answer 1

Solution:

The price of a share of a firm is calculated using the following formula:

P = D₁ / ( k_e – g )

Where

P = Price of the share;      D₁ = Dividend per share payable next year i.e., one year from now ;

g = growth rate ;

k_e = Required Rate of return of stock

As per the information given in the question we have ;

P = $ 50    ;    D₁ = $ 2.00   ;    k_e = 12.00 % = 0.12    ;    g = To find

Applying the above values in the formula we have

50 = 2 / ( 0.12 – g )

( 0.12 – g ) = 2 /50

0.12 – g = 0.0400

g = 0.12 – 0.0400 = 0.0800

g = 8 %

Thus the growth rate of the dividend = 8 %

The solution is Option 3 = 8 %